Bayesian Joint Matrix Decomposition for Data Integration with Heterogeneous Noise

TL;DR

This paper introduces a Bayesian joint matrix decomposition method that explicitly models heterogeneous noise across multiple data sources, improving data integration and pattern discovery in multi-view datasets.

Contribution

It proposes a novel Bayesian framework (BJMD) for joint matrix decomposition that accounts for noise heterogeneity, with scalable algorithms for practical application.

Findings

BJMD outperforms existing methods on synthetic datasets.

BJMD is competitive on real-world data.

The variational Bayesian algorithm effectively utilizes posterior distributions.

Abstract

Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single source. However, it is common that data are from different sources with heterogeneous noise. A few of matrix decomposition methods have been extended for such multi-view data integration and pattern discovery. While only few methods were designed to consider the heterogeneity of noise in such multi-view data for data integration explicitly. To this end, we propose a joint matrix decomposition framework (BJMD), which models the heterogeneity of noise by Gaussian distribution in a Bayesian framework. We develop two algorithms to solve this model: one is a variational Bayesian inference algorithm, which makes full use of the posterior distribution; and another is a maximum a posterior algorithm, which is more scalable and can be easily paralleled. Extensive experiments on synthetic and real-world datasets demonstrate that BJMD considering the heterogeneity of noise is superior or competitive to the state-of-the-art methods.